Algebra of the income expenditure model Consider a small economy that is dosed t

Question

Algebra of the income expenditure model Consider a small economy that is dosed to trade, so its net exports are equal to zero. Suppose that the economy has the following consumption function, where C is consumption, Y is real GOP, I is investment. G is Government purchases, and T is for net taxes. Suppose G - $130 billion, I - $60 billion, and T - $20 billion. Given the consumption function and the fact that, in a dosed economy, total expenditure can be calculated as Y - C +/+G, the aquarium output level is billion. Suppose the government purchases are reduced by $100 billion. The new equilibrium level of output will be equal to billion. Based on the effect of the change in government purchases on equilibrium output, you can tell that this economy's spending multiplier is equal to

Explanation / Answer

Y = C + I + G

Y = 25 + 0.75 ( Y-T) + $ 60 + $ 130

Y = 25 + 0.75 Y - 0.75 T + $ 60 + $ 130

0.25Y = 25 - 0.75T + $ 60 + $ 130

0.25Y = 25 - 0.75 X $ 20 + $ 60 + $ 130

Y = $ 800 billion [ Equilibrium output level]

If government purchases are reduced by $ 100 billion

0.25Y = 25 - 0.75 X $ 20 + $ 60 + $ 30 billion

Y = $ 400 billion [ New Equilibrium output level]

Spending multiplier = 1 / ( 1 - MPC)

MPC = Marginal propensity to consume

MPC = Change in government purchases / Change in equilibrium output level

MPC = $ 100 billion / $ 400 billion

MPC = 0.25

Spending multplier = 1 / 1 - MPC

Spending multiplier = 1 /( 1 - 0.25)

Spending multiplier = 1.33

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